The most beautiful equation is... Euler's identity

Euler has been described as the "Mozart of maths". His most famous equation links all the most important numbers

"Most of modern mathematics and physics derives from work of Leonhard Euler," says Robin Wilson of the Open University in the UK. He was "the most prolific mathematician of all time" and "the Mozart of mathematics". But for all his achievements, "many so-called educated people have never heard of him."

His most famous single equation is Euler's identity. It is said to be the equation that can link all of the constants of mathematics together.

The equation combines five of the most important numbers in mathematics. These are:

  • 1 – the basis of all other numbers
  • 0 – the concept of nothingness
  • pi – the number that defines a circle
  • e – the number that underlies exponential growth
  • i – the "imaginary" square root of -1

The numbers all have many practical applications, including communication, navigation, energy, manufacturing, finance, meteorology and medicine.

But that's not all. Euler's identity also contains the three most basic mathematical operations: addition, multiplication and exponentiation.

"Euler's identity is amazing because it is simple to look at and yet incredibly profound," says David Percy of the University of Salford in the UK – who could not choose between this and Bayes' theorem. "What appeals to me is that this equality connects some incredibly complicated and seemingly unrelated concepts in a surprisingly concise form."

Read more: What is the most beautiful equation?